AutoStep: Locally adaptive involutive MCMC

Tiange Liu, Nikola Surjanovic, Miguel Biron-Lattes, Alexandre Bouchard-Cote, Trevor Campbell
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:39624-39650, 2025.

Abstract

Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods—AutoStep MCMC—that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that under mild conditions AutoStep MCMC is $\pi$-invariant, irreducible, and aperiodic, and obtain bounds on expected energy jump distance and cost per iteration. Empirical results examine the robustness and efficacy of our proposed step size selection procedure, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-liu25br, title = {{A}uto{S}tep: Locally adaptive involutive {MCMC}}, author = {Liu, Tiange and Surjanovic, Nikola and Biron-Lattes, Miguel and Bouchard-Cote, Alexandre and Campbell, Trevor}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {39624--39650}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/liu25br/liu25br.pdf}, url = {https://proceedings.mlr.press/v267/liu25br.html}, abstract = {Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods—AutoStep MCMC—that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that under mild conditions AutoStep MCMC is $\pi$-invariant, irreducible, and aperiodic, and obtain bounds on expected energy jump distance and cost per iteration. Empirical results examine the robustness and efficacy of our proposed step size selection procedure, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.} }
Endnote
%0 Conference Paper %T AutoStep: Locally adaptive involutive MCMC %A Tiange Liu %A Nikola Surjanovic %A Miguel Biron-Lattes %A Alexandre Bouchard-Cote %A Trevor Campbell %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-liu25br %I PMLR %P 39624--39650 %U https://proceedings.mlr.press/v267/liu25br.html %V 267 %X Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods—AutoStep MCMC—that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that under mild conditions AutoStep MCMC is $\pi$-invariant, irreducible, and aperiodic, and obtain bounds on expected energy jump distance and cost per iteration. Empirical results examine the robustness and efficacy of our proposed step size selection procedure, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.
APA
Liu, T., Surjanovic, N., Biron-Lattes, M., Bouchard-Cote, A. & Campbell, T.. (2025). AutoStep: Locally adaptive involutive MCMC. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:39624-39650 Available from https://proceedings.mlr.press/v267/liu25br.html.

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